Cash for Clunkers - Department of Economics

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					               Evaluating “Cash for Clunkers”: Program Effects on
                          Auto Sales, Jobs, and the Environment


                               Shanjun Li, Joshua Linn, and Elisheba Spiller1




                                                   Abstract

       We investigate the effects of “Cash for Clunkers”, a $3 billion economic stimulus
       program, on new vehicle sales, employment, gasoline consumption, and the environment.
       Using Canada as the control group in a difference-in-differences framework, we find that
       the program increased new vehicle sales by about 0.39 million during July and August of
       2009, while the net increase reduced to 0.25 million from June to December. The
       difference suggests that, as intended, the program significantly shifted sales to July and
       August from other months. Nevertheless, the program would result in only 8.58 to 28.28
       million tons of CO2 emission reductions, implying a cost per ton ranging from $91 to
       $301 even after accounting for the benefit of the program in reducing criteria pollutants.
       In addition, the program is estimated to have created 3,676 job-years in the auto assembly
       and parts industries during June-December of 2009, and the effect decreased to 2,050 by
       May 2010.




1 Shanjun Li and Joshua Linn are fellows at Resources for the Future, 1616 P Street NW, Washington DC
20036. Elisheba Spiller is a PhD candidate in the Department of Economics, Duke University, Durham, NC
27708-0097. We thank Soren Anderson, Antonio Bento, Maureen Cropper, Robert Hammond, and Kevin Roth
for helpful comments and Jeffrey Ferris and Marissa Meir for excellent research assistance. Authors’ emails are:
li@rff.org, linn@rff.org, and elisheba.spiller@duke.edu.
                                                         1
1. Introduction

Amid the worst economic recession in the United States since the Great Depression, Professor Alan
Blinder in a July 2008 Op-Ed article in the New York Times stated that “Cash for Clunkers is the best
stimulus idea you have never heard of.” Officially launched exactly a year later by the Obama
administration, with several modifications, the Cash for Clunkers program provided eligible consumers
a $3,500 or $4,500 rebate when trading in an old vehicle and purchasing or leasing a new vehicle. The
program had two goals: to provide stimulus to the economy by increasing auto sales, and to improve the
environment by replacing old, fuel-inefficient vehicles with new, fuel efficient ones. During the
program’s nearly one-month run, it generated 678,359 eligible transactions and had a cost of $2.85
billion. The program received enormous media attention: while many considered the program as a great
success, some viewed the program as being ineffective and inefficient in achieving the economic and
environmental goals.2

     While several other studies have analyzed particular aspects of the program, this study estimates
the composition of the fleet of vehicles that would have been sold in the absence of the program, which
permits a comprehensive evaluation of the program effect on vehicle sales, the environment and
employment. First, we examine its effects on new vehicle sales both during the program and in the
several months before and after the program. Many observers of the program were concerned that it
would primarily pull demand from adjacent months, and therefore it would provide little short-term
stimulus and even less in the longer term. Consequently, we focus on two types of changes in consumer
behavior caused by the program: switching from purchasing low fuel-efficiency to high fuel-efficiency
vehicles, and shifting the purchase time to take advantage of the program’s incentives.

     Second, we evaluate the program’s cost-effectiveness in reducing gasoline consumption and
carbon dioxide (CO2) emissions by comparing total gasoline consumption as well as in emissions of
CO2 and criteria pollutants with and without the program. There exist many federal subsidy programs
aiming to reduce U.S. gasoline consumption and CO2 emissions such as tax credits for ethanol blending
and income tax incentives for hybrid vehicles purchases. The cost-effectiveness analysis permits a
comparison across the different programs.



2Transportation Secretary LaHood declared the program to be “wildly successful” at the end of the program,
while two Op-Ed articles in the Wall Street Journal on August 2nd and 3rd raised doubts about whether the
program truly increased sales and stimulated the economy. They argued that the program would most likely
result in the shifting of future vehicle demand to the present and could hurt the sales of other goods.
                                                          2
     Third, we examine the effects of the program on employment in the vehicle production and
assembly industries. Creating jobs by increasing auto sales was another primary goal of the program.
We evaluate the program effectiveness in this aspect in two steps: 1) we estimate the marginal
relationship between vehicle production and hours worked; and 2) we combine these estimates with the
estimated program effects on vehicles sales to obtain the effect of the program on employment.

     The basis for these evaluations is the difference-in-differences (DID) analysis in a vehicle demand
framework based on monthly sales of new vehicles by model from 2007 to 2009. The U.S. market
constitutes the treatment group in the analysis. We use Canada as the control group based on two
observations as well as some statistical evidence. First, Canada did not have a Cash for Clunkers-type
program similar to that in the U.S., while nearly a dozen European countries did in 2008 and 2009.
Second, the Canadian auto market is probably the most similar to the U.S. market: in both countries in
recent years before the recession, about 13-14 percent of households annually purchased a new vehicle;
characteristics of vehicles sold are similar; and pre-program time trends are similar.

     The DID analysis shows that the program increased sales of vehicles that were eligible for the
rebate (eligible vehicles) and lowered sales of ineligible vehicles during the program period.
Furthermore, within eligible vehicles, the positive effect was larger for those with higher fuel efficiency
– which yield a higher rebate. The negative effect on ineligible vehicles was stronger for those that
barely missed the eligibility requirement, implying that the program caused consumers to substitute from
these vehicles to eligible vehicles. We find that the program resulted in lower sales in the months before
and especially after the program, and that the effect on sales weakened over time. The empirical results
thus suggest that the program resulted in consumer demand shifting from ineligible vehicles to eligible
ones as well as shifting from pre- and post-program periods to program periods, with the inter-temporal
shift having the strongest impact.

     With the parameter estimates from the DID analysis, we simulate vehicle sales in the counterfactual
scenario of no program. Of the 0.66 million vehicles purchased under the program, 0.28 million would
have been purchased anyway, either the few weeks before, during, or the week after the program. Thus,
the program resulted in a sales increase of only 0.39 million during July and August of 2009. The
program effect on vehicle sales eroded further when we look at a longer time horizon: the increase in
vehicle sales during June to December of 2009 was 0.25 million. In addition, our simulation results
show that Toyota, Honda and Nissan benefited from the program disproportionally more than other



                                                     3
firms: with a combined market share of around 37 percent before the program, they accounted for about
50 percent of the increased sales.

     Based on the simulation results on vehicle sales, we estimate the differences in total gasoline
consumption, CO2 emissions, and four criteria pollutant emissions (carbon monoxide, volatile organic
compounds, nitrogen oxides and exhaust particulates) with and without the program. We provide the
results for 12 different cases, across which parameter and behavior assumptions vary. The total
reduction in gasoline consumption ranges from 884 to 2916 million gallons while that in CO2 emissions
ranges from 8.58 to 28.28 million tons. After accounting for the program’s benefit in reducing criteria
pollutants, we estimate that the program’s cost of CO2 emissions reduction ranged from $91 to $294 per
ton while that of gasoline consumption reduction ranged from $0.89 to $2.92 per gallon.

     To examine program effects on employment, we first examine the marginal relationship between
vehicle production and hours worked. Together with the results on vehicle sales, we show that the short-
run (June – December 2009) effect of the program on total employment is 3,676 job-years and is
roughly split between the assembly and parts industries. For comparison, the estimated sales effect is
246,000 vehicles, which implies that approximately one job-year was created for every 67 vehicles sold
under the program. The long-run effect, over June 2009-May 2010, is approximately half the short-run
effect, or 2,050 job-years.

     Several recent studies have evaluated particular aspects of the Cash for Clunkers program. Knittel
(2009) estimates the implied cost of the program in reducing CO2 emissions. Council of Economic
Advisors (CEA 2009) and Cooper et al. (2010) analyze program impacts on vehicle sales and
employment. National Highway and Traffic Safety Administration (NHTSA, 2009) also examines
program effects on gasoline consumption and the environment. The major difference between our
analysis and the aforementioned studies lies in the fact that we use the DID approach to estimate
counterfactual sales by vehicle model in the absence of the program. Knittel (2009) does not establish
the counterfactual and does not examine program effects on vehicle sales. The other three studies
estimate the sales effect based on heuristic rules and aggregate sales data and do not examine consumer
substitutions across models and over time.

     We find a smaller cost per ton of CO2 reduction than Knittel (2009) because we account for the
difference between total CO2 emissions during the remaining lifetime of the trade-in vehicles and the
emissions from the new vehicles purchased to replace them, and the fact that the whole fleet of new
vehicles purchased in the presence of the program would be more fuel efficient than that without the
                                                   4
program; Knittel (2009) only considers the first effect. Compared with the three studies that examine
program effects on employment, our analysis is based on the marginal rather than average relationship
between vehicle production and hours worked. Focusing on changes in employment and production is
more likely to reveal the relationship of interest than simply computing the average ratio of production
to employment in a single year, as in CEA. In addition, we believe that using production worker hours is
more appropriate than total employment, which is the metric used in NHTSA, because hours are more
likely to respond to changes in production.

        The rest of the paper is organized as follows. Section 2 describes the program and the data in detail.
It also presents a discussion on Canada serving as the control group for the U.S. Section 3 lays out the
empirical framework. Section 4 provides estimation results and analyzes the program effect on auto
sales. Section 5 examines the program impact on gasoline consumption and CO2 emissions. Section 6
estimates the program effect on employment and Section 7 concludes.


2. Background and Data

In this section, we first discuss the background of the program, including the timeline and eligibility
rules. Next, we present the data sets that are used in the empirical analysis. We then provide some casual
evidence supporting the use of Canada as the control group, with statistical evidence provided in Section
4.


2.1 Program Description

As Figure 1 shows, the Consumer Assistance to Recycle and Save Act (CARS) was passed by the House
of Representatives on June 9th, 2009 and by the Senate on June 18th, and was signed into law by the
President on June 24th. This law established the Cash for Clunkers program, a temporary program
granting subsidies to car owners who trade in their older, fuel inefficient vehicles to purchase a new and
more efficient vehicle. The traded-in vehicle would then be dismantled in order to ensure that it does not
return to the road. The program was officially launched on July 27th, 2009 and terminated ahead of
schedule on August 25th, 2009. It generated 678,359 eligible transactions at a cost of $2.85 billion. 3
Originally, the program was planned as a $1 billion program with an end date of November 1st, 2009.




3   Statistics are from press releases at http://www.cars.gov/official-information.
                                                           5
      The Cash for Clunkers program was intended to help reduce the number of old and less fuel
efficient vehicles (i.e. clunkers) on the roads as well as shift demand towards more fuel efficient new
vehicles. The program outlined four requirements that the trade-in would have to meet in order to be
eligible, as shown in Table 1A. The requirements vary according to the size and class of the vehicle. The
first three requirements ensured that the traded-in vehicle would otherwise be on the road had it not been
for the program: the trade-in vehicle must be drivable; it must have been continually insured and
registered by the same owner for the past year; and it must not be older than 25 years for all vehicles
except for category 3 vehicles. The fourth rule ensured that the vehicle is in fact a “clunker”: it must
have a combined fuel efficiency of 18 mpg or less for all vehicles except category 3 trucks. 4



                         Figure 1: Timeline of the Cash for Clunkers Program

     June 9        June 24           July 27                       August 25
    “C-f-C”        President         CARS program                  CARS program
     approved      signed CARS       officially launched           ends
     by House                        by NHTSA

       June 18             July 24                                     November 1
       Bill approved       Final rules                                 Projected
       by Senate           issued                                      end date



                Pre-Program Period           Program Period              Post- Program Period




      Table 1B shows the minimum MPG the new vehicle needed to qualify. The MPG requirement was
22 for passenger automobiles, 18 for category 1 trucks, and 15 for category 2 trucks. Category 3 trucks,
on the other hand, had no minimum fuel efficiency requirement, but they could only be traded in for
category 3 trucks. Finally, the MSRP of the new vehicle could not exceed $45,000.Table 1B shows that
the stringency of the MPG requirement is greatest for passenger cars, and decreases across the truck
categories. For example, a new passenger car must have an MPG improvement of at least 4 over the
trade-in vehicle in order to qualify for the $3,500 rebate while a 10 MPG improvement is needed for the


4
 Category 1 trucks are “non-passenger automobiles” including SUVs, medium-duty passenger vehicles,
pickup trucks, minivans and cargo vans. Category 2 trucks are large vans or large pickup trucks whose
wheelbase exceeds 115 inches for pickups and 124 for vans.
                                                     6
$4,500 rebate. For a new vehicle in category 1, the requirements on the MPG improvement is 2 and 5 for
the two rebate levels. The requirements become still less stringent for category 2 and 3 vehicles.


2.2 Data Description

We collect data on monthly vehicle sales for all models in the U.S. and Canada from 2007 to 2009 from
Automotive News. We combine these data with vehicle MPG data from the Environmental Protection
Agency’s fuel economy database as well as vehicle prices and other characteristics from Wards’
Automotive Yearbook. Our data include 16,814 observations of monthly vehicle sales. We define a
model as a country-vintage-nameplate (e.g., a 2007 Toyota Camry in U.S.) and we have 1,436 models in
the data. Almost all the models sold in Canada are available in the United States.

     Panel 1 in Table 2 provides summary statistics of the data set. Based on the eligibility rules, 1,008
of the 1,436 vehicle models meet the requirement and could be eligible for the rebate during the program
(henceforth, eligible vehicles). Among the 16,814 observations, about 70 percent of sales in both
countries are for eligible vehicles. As shown in the table, the eligible vehicles have much higher sales
than ineligible ones. Although the average sales per model in the U.S. are much higher than in Canada,
the number of new vehicles sold per households is 13-14 percent in both countries. On average, the
eligible vehicles are cheaper and, by definition, more fuel-efficient than ineligible ones. The average
prices are very similar in the two countries across both categories. Because a higher proportion of light
truck models is available in Canada, the average fuel efficiency of models sold in Canada in both
categories is lower than in the U.S. Nevertheless, the sales-weighted MPG of new vehicles is higher in
Canada, likely due to higher gasoline prices and lower average household income.

     Panel 2 of Table 2 presents summary statistics of monthly averages of the gasoline price, interest
rate, and consumer confidence index in the two countries. All three variables are higher on average in
Canada than in the U.S. The interest rate in the U.S. is for new car loans at auto finance companies
(average duration about 60 months), while due to the lack of the same data series, we collect the five-
year personal mortgage rate in Canada. The consumer confidence index for the U.S. is from the
Conference Board consumer confidence survey while that for Canada is by the Conference Board of
Canada. Past studies have shown that consumer confidence surveys have good predictive power of
future spending (e.g., Carroll, Fuhrer and Wilcox 1994; Bram and Ludvigson 1998; and Ludvigson
(2004)). We use the data discussed so far to estimate the effect of the program on vehicle sales. To
examine the effectiveness of the program on energy consumption and the environment, we use the
                                                    7
public database for the Cash for Clunkers program from www.cars.gov. The data set provides (dealer-
reported) information on the trade-in and new vehicles for each transaction during the program. There
are 678,539 transactions in the data set. We remove transactions that are subject to reporting error (e.g.,
MPG information out of eligible range). In addition, we delete 2,278 category 3 vehicles and 6,169
leased vehicles in order to be consistent with our demand analysis on new vehicles. After removing
18,959 records, there are 659,400 observations of trade-in and new vehicles under the program.

     To estimate the program effect on employment, we use historical data from the Bureau of Labor
Statistics (BLS) on monthly employment and average weekly hours at parts and assembly plants.
Production worker hours are calculated by multiplying average weekly hours * monthly employment * 4.
Data on total vehicle production are obtained from the Federal Reserve Board (FRB).

     Table 3 shows the summary statistics on trade-in and new vehicles. This table demonstrates that
consumers were trading in more light trucks than cars, and that these trucks were both more fuel
inefficient and newer. Furthermore, the average rebate amount is $4,214 and the total payment on these
vehicles is $2.78 billion (out of $2.85 billion on all transactions).


2.3 Canada as the Control Group

To examine the effect of the program, we employ a difference-in-differences (DID) approach as
discussed in more detail in the next section. The key to this approach entails finding a control group that
provides an unbiased estimate of what would have happened to the treatment group in the absence of the
program. We believe that Canada can serve as the control group based on the following observations,
with more statistical evidence provided in Section 4.

     First, Canada did not have a Cash for Clunkers program similar to that in the U.S., whereas many
European countries including Germany, France, Italy and Spain did in 2008 and 2009. Although Canada
has a Retire Your Ride Program that started in January 2009, the program is not comparable to the Cash
for Clunkers program for at least three reasons. First, the program provides only CA$300 worth of credit
for eligible participants (owners of 1995 or older model year vehicles that are in running condition),
compared to $3,500 or $4,500 offered in the US. Second, the sole goal of the program is to improve air
quality by encouraging people to use environmentally-friendly transportation, so the program is not tied
to new vehicle purchases. Depending on the province, the credit can be a public transit pass, a
membership to a car-sharing program, cash, or a rebate on the purchase of a 2004 or newer vehicle.


                                                       8
Third, the program only retired about 60,000 vehicles during the first 15 months. Therefore, its effect on
new vehicle sales (about 1.6 million annually) should be negligible.

     The second justification for using the Canadian auto market as the control group is that it is
probably the most similar to the U.S. market. About 13-14 percent of households purchased a new
vehicle in recent years before the economic downturn in both countries. Table 2 also shows that the
vehicles sold are similar in characteristics, although the U.S. market has a larger set of models. Figure 2
depicts monthly sales of new vehicles in the two countries from 2007 to 2009. The top graph plots total
monthly sales in logarithm and the bottom graph shows the demeaned sales per 1000 people. To remove
seasonality, the sales are demeaned using the monthly averages from 2007-2008. Therefore, the flatter
the line is, the less volatile are year-to-year changes in sales. The bottom graph illustrates that the
month-to-month trends in vehicle sales in the two countries are similar before July 2009. The two lines
intersect around January 2008 because the sales in 2008 dropped more sharply in the U.S. than in
Canada. The larger sales decline in the U.S. is consistent with the larger increase in the interest rate and
steeper decline in consumer confidence levels, as shown below in Figures 6-8. In early 2009, the
economic downtown appears to have had a more severe negative effect on the U.S. auto market than on
Canada. This could be caused by the sharper decrease in consumer confidence in the U.S. (see Figure 7).

    Figure 3 shows monthly sales of eligible vehicles for the two countries from 2007 to 2009. Both the
top and bottom plots display very similar patterns to those in Figure 2, partly due to the fact that eligible
vehicles account for over 80 percent of total new vehicle sales. The two graphs in Figure 4 are for
ineligible vehicles. These plots show that the month-to-month sales trends are similar in the two
countries for ineligible vehicles, although there is not a dramatic difference in population denominated
sales after removing seasonality. It is interesting to note that although sales of ineligible vehicles did not
decrease during the program period, the sales after removing seasonality decreased, which is consistent
with the hypothesis that demand shifted from ineligible vehicles to eligible vehicles during the program
period.

     Figure 5 plots monthly gasoline prices in the two countries. Because the gasoline price is largely
determined by the world market, the difference between the two series is quite stable over time. The
difference in monthly interest rates shown in Figure 6 is much more volatile, especially during the
second half of 2008. Figure 7 shows the consumer confidence index in the two countries. Although
consumer confidence was similar in early 2007, it experienced a more dramatic decline between late
2007 and early 2009 in the U.S.

                                                      9
     We note that although there are some differences between the two countries, we try to account for
these differences by incorporating observed demand factors (e.g., gasoline prices) in the regressions. In
addition, we control for some of the unobserved demand factors using country fixed effects. Our hope is
that demand factors that are left uncontrolled are similar in the two countries or do not significantly
affect vehicle demand. To show after the effect of controlling for observed demand factors (gas price,
interest rate and consumer confidence) as well as seasonality, Figure 8 depicts the predicted vehicle
sales (in logs) for eligible and ineligible vehicles after removing the effect of these factors.5 The two
plots show that, after removing the effect of observed demand factors, the trends of vehicle sales in the
two countries track each other closely. We provide more discussion on this point Section 3 and present
statistical evidence on the validity of using Canada as the control group in Section 4.


3. Empirical Strategy

In this section, we first discuss the channels through which the program could affect vehicle sales. We
then describe our empirical model.


3.1 Potential Program Effects

In our main analysis, we define the pre-program period as June 9th to July 26th, 2009. Although some
consumers may have known about the bill before the House passed it on June 9th, we expect that the
uncertainty surrounding the eligibility requirements as well as the bill’s final passage would greatly limit
its effect before June 9th. The program period is defined from July 27th to August 25th. Although the
program retrospectively recognized qualified sales from July 1st until the official start date, the total
number of these sales was only 30,317, which is less than the average daily sales during the first week of
the program. Sensitivity analysis shows that our results are robust to alternative definitions of the pre-
program and program periods.

     Because an automobile is a durable good, the program could affect vehicle sales before, during, or
after the program period. During the program period, some consumers who would have purchased an
ineligible model or chosen not to purchase a new vehicle may choose to purchase an eligible model
instead. In addition, the program could result in consumers changing the purchase time in order to


5The dependent variable is monthly sales by model in logarithm. The control variables are the same as those in
equation (6) without including the variables capturing the program effect. The regression includes data from
January 2007 to May 2009 (i.e., before the program could affect vehicle sales).
                                                      10
coincide with the program period (i.e., intertemporal substitution). In the absence of the program, these
consumers could have purchased an eligible or an ineligible vehicle in other periods. The graph above
illustrates the different substitution channels.



        Choices \ Timing            Pre-program      Program            Post-program
                                    06/09-07/26      07/27-08/25        08/26-

        Ineligible Vehicle


        Eligible Vehicle


        No Purchase



    The degree of these substitutions could vary over product space as well as over time for several
reasons. First, there could be a stronger substitution to eligible vehicles from vehicles that barely miss
the MPG requirement, compared to the substitution from vehicles that have much lower fuel efficiency.
In addition, because high MPG vehicles could be eligible for a higher rebate ($4,500 versus $3,500) the
program could have a stronger effect on the vehicles eligible for the higher rebate. Second, the
substitution could exhibit heterogeneity over time. For example, the intertemporal substitution could be
stronger right before or after the program than farther away from the program. Moreover, because the
length of the program is not fixed and runs out when the designated amount of stimulus money is used
up, the program could have a stronger effect at the beginning of the program period. In fact, the initial
one billion dollars were used up within a week while the additional two billion dollars lasted for three
weeks. In the estimation, we try to capture these effects by allowing for heterogeneity across vehicles
and over time.


3.2 Empirical Model

We implement the difference-in-differences method in a regression framework where the Canadian auto
market is used as the control group for the U.S. market. The regression model is based on monthly sales
of new vehicles. Let c index country (U.S. or Canada), t index year, m index month, and j index vehicle
model. We define a vehicle model as a country-vintage-nameplate (e.g., a 2009 Ford Focus in the U.S.)
                                                   11
in order to account for changes in product attributes over years and across countries for the same
nameplate as well as country-specific taste differences. We estimate the following linear model as the
starting point of our analysis:

      J    J            #H              -   ${   .H         {           -    %H                -   &{   .H   {
                                    -            -       -          -        -             ,                     (1)

where J        is the sales of vehicle model j. 6 H          is the eligibility dummy, equal to one for any vehicle
in either country that meets the program requirement (irrespective of whether the program is in effect)
and 0 otherwise.             is the number of effective days during the program period in month m, as
defined below. The use of effective days instead of the nominal number of days allows the program
effect to vary over the program period.7 We use the geometric function and the logit function to model
the growth (or decay) of the program effect. Assuming geometric growth, the number of effective days
in month m during the program period is:


                                                                        (#    #,                                              (2)

where k is the kth day into the program. H           is the total number of program days in month m . It is 5 and
25 in July and August 2009 in the U.S., and 0 in all the other months in our main regressions.                         # is   the
parameter to be estimated. Similarly, for the logistic growth, the number of effective days is:

                                                                           #
                                                                    (# # ?L {      {
                                                                                       .                                      (3)


               is the number of effective days pre- or post-program. In order to allow the time path to be
different during the pre-program period and post-program period, we include separate parameters for the
pre- and post-program periods. In the geometric case, the number of effective days is:


                                                                $   ”‡ . ’”‘‰”ƒ ‹ –Š‡  
                                                 |      (#
                                                                                                                              (4)
                                                       (#       %   ‘•– . ’”‘‰”ƒ ‹ –Š‡  

6 For all the regressions presented in the paper, we also estimate a multinomial logit model in the linear form
(Berry 1994) where we assume that consumers have a total of J vehicle models plus an outside good indexed by
0 (i.e., not purchasing a new vehicle) to choose from in a given month. The dependent variable is Ž‘‰ {      {.
Ž‘‰ {      " { with      and     " being the market shares of model j and the outside good that captures the
decision of not purchasing a new vehicle respectively. The market size is the number of households in the two
countries. The results are very close to the results from the linear models shown in Section 4.
7 Because the program period started in late July and ended in late August in 2009, the use of month dummies

would not allow us to disentangle the program effect for different time horizons.
                                                         12
where for the pre-program period, H          is 22 and 26 in June and July 2009 in the U.S. and zero for all
other months. For the post-program period, H          is 6 for August 2009 and the nominal number of days
for the months thereafter. For the logistic time path,              is defined similarly.

            is a vector of product attributes as well as their interactions with gasoline price, the interest
rate, and the consumer confidence index. Further, we allow the three variables to have different effects
in the two countries (by interacting them with country dummies).                        denotes model (i.e., country-
vintage-nameplate) fixed effects, which control for unobserved vehicle attributes as well as country-
specific taste differences at the model level.       are year-month fixed effects that control for year-month
unobservable demand shocks common to the two countries.                     are country-month fixed effects, which
control for country specific seasonality.          is the random demand shock.

     The first two variables on the right-hand side of equation (1) capture the program effect on vehicle
sales during the program period while the next two variables capture the program effect pre- and post-
program. One would expect the coefficient on the first variable to be positive and that on the second
variable to be negative given the expectation that the program would increase the sales of eligible
vehicles and reduce the sales of ineligible vehicles. The third and fourth coefficients should both be
negative due to intertemporal substitution, although one would expect the intertemporal substitution
from ineligible vehicles to eligible vehicles to be weaker than that between eligible vehicles.

    The above specification assumes that the program would have the same effect on vehicles in the
same eligibility category. However, this would not likely hold for two reasons. First, there are two rebate
levels ($3,500 and $4,500) and the eligibility depends on the difference between the MPG of the new
vehicle and that of the trade-in vehicle. The effect on eligible vehicles with high MPGs could be
stronger than on those with low MPGs since high MPG vehicles are more likely to be eligible for the
$4,500 rebate. Second, consumers are more likely to switch from these barely ineligible vehicles to
eligible vehicles than from other vehicles. Due to the trade-off between vehicle size/horsepower and fuel
efficiency, to go from barely ineligible vehicle to eligible ones, consumers likely suffer a smaller
sacrifice in vehicle size or horsepower than from vehicles that are far below the MPG requirements. In
order to incorporate these heterogeneous effects, we estimate the following model:

                        J   J           #H                -    $H              É       H       É
                                    -   %{    .H      {            -   &{   .H      {           É   H   É
                                    -   'H                -    H             É     H       É

                                                          13
                                   -    { .H         {                -   { .H       {           É   H   É
                                       -             -            -       -   -          ,                          (5)

where     H is gallons per mile and          H           H        .       H   .H         is the MPG requirement for
rebate eligibility, which varies across vehicle categories as discussed in Section 2.1. The larger
    H       is, the farther the vehicle’s fuel efficiency is from the requirement. The additional variables
allow the program effect to depend on vehicle fuel efficiency. For example, a positive coefficient on the
second variable would imply that the sales increase is larger for eligible vehicles with high MPGs.
Similarly, a negative coefficient on the fourth variable would mean that the sales decrease is larger for
vehicles that barely miss the MPG requirement than for other ineligible vehicles.


3.3 Identification

Our empirical models control for unobservables in several dimensions by including model fixed effects
    , common time effects       , and country-specific seasonality               . In addition, we include demand-
side variables and their interactions with vehicle characteristics to control for differences in vehicle
demand in these two countries. Nevertheless, the unbiasedness of coefficient estimates hinges on the
identifying assumption that time trends in demand and supply are the same in the two countries.
Otherwise, we risk interpreting preexisting differences in time trends as the effect of the program.

     The common trend assumption is important given the fact that the auto markets in the two countries,
although similar, exhibit differences (see Figures 2-7). This identifying assumption cannot be directly
tested, but we can take advantage of the data before the pre-program period to test for differences in pre-
existing trends. If they were the same before the program, one would be more comfortable in assuming
that they are the same afterwards. This strategy has been used in many previous studies that have data
for multiple periods before the treatment (e.g., Eissa and Liebman 1996; Galiani, Gertler and
Schargrodsky 2005).

     The test can be carried out by estimating a modified version of equation (1) using the data before
June 2009, excluding the first four terms, and adding country-month dummies interacted with the
eligibility dummy:

                           J   J         H       H            #   -{ .H       {H             $

                                       -             -            -       -      -       ,                    (6)

                                                         14
where H        is a vector of 4 U.S.-month dummies for February-May in 2009. The January dummy and
the corresponding dummy variables for Canada are absorbed by model fixed effects               , together with
time trends     . Large estimates of   #   and   $   would imply differences in pre-existing trends across the
U.S. and Canada.


4. Estimation Results

We first present the test results for the common trend assumption. We then show the estimation results
for a variety of specifications.

4.1 Examining Common Trend

Figures 2 to 4 show that monthly sales of new vehicles in the two countries exhibit similar trends before
the program. We now provide statistical evidence on the common trend assumption by using the
regression results for equation (6) to examine if the trends are the same in the two countries from
February to May 2009, for each of the two groups of vehicles. Table 4 presents parameter estimates
where the first specification includes the fewest control variables while the fourth specification includes
the most. The first four parameters are for eligible vehicles while the next four are for ineligible vehicles
for each of the four months. If the trends are the same in the two countries, these eight parameters
should not be statistically different from zero.

     The first specification includes model fixed effects that control for unobserved model attributes as
well as (time-invariant) model-specific demand shocks. The specification, however, does not control for
the effect of potentially important demand factors such as the interest rate and consumer confidence
level, nor does it control for common time trends or seasonality in vehicle demand. The estimation
results show that several of the first eight parameters are statistically different from zero at the 5%
confidence level. This suggests that demand shocks left uncontrolled by the variables in the model affect
vehicle sales differently in some of the four months across the two countries.

     The second specification includes eight economic variables in addition to the variables in the first
specification. These eight variables are the monthly interest rate, consumer confidence index, their
interactions with vehicle price, as well as interactions of the previous four variables with country
dummies. The third specification adds fixed effects for common time trends and country-specific
seasonality. In both the second and third specifications, some of the first eight parameters are still
statistically different from zero.
                                                         15
     In the fourth specification, we include the eight economic variables from the second specification
and the additional fixed effects from the third specification. None of the first eight parameter estimates
is statistically significant at any conventional confidence level. We also note that the coefficients are not
economically significant when compared to the program effects given by the parameter estimates
discussed in the next section. The comparison across the specifications shows the importance of
controlling for the observed differences in the demand factors as well as the unobserved ones (e.g.,
through fixed effects) in the demand analysis. In the benchmark model for DID regressions below, we
include the same control variables as those in the fourth specification.


4.2 Difference-in-Differences Results

We estimate parameters in equations (1)-(5) using the Generalized Method of Moments (GMM).
Equation (1) does not allow for heterogeneous effects across models in the same eligibility category. In
estimating the model, the first four variables in equation (1) are updated during each parameter iteration
following equations (2)-(4). The exclusion restrictions used are month dummies for June-December of
2009 interacting with the eligibility dummy and the ineligibility dummy. This implies 14 exclusion
restrictions and 10 over-identification moments. For equation (5), the first eight variables are updated
iteratively during estimation. The exclusion restrictions are the 7 month dummies (June-December of
2009) interacting with the eligibility dummy, the ineligibility dummy, the eligibility dummy*|∆GPM|,
and the ineligibility dummy*|∆GPM|. This gives 28 exclusion restrictions and 20 over-identification
moments.

    Table 5 reports parameter estimates and standard errors for three specifications where the time
effect is modeled using the geometric function. The first specification is for equation (1) while the next
two specifications are for equation (5). The first two coefficients in the first specification capture the
effect of the program during the program period. Both are statistically significant at the 1% confidence
level and they suggest that the program increased the sales of eligible vehicles while reducing the sales
of ineligible vehicles. The next two coefficients capture the effect of the program before and after the
program: the program decreased the sales of eligible vehicles but the effect on ineligible vehicles was
not statistically significantly different from zero, suggesting that the reduction in vehicle sales through
intertemporal substitution occurs primarily among eligible vehicles.

    The second and third specifications in Table 5 allow the program to have different effects for
vehicles within the same eligibility category by including interaction terms between eligibility status and
                                                     16
|∆GPM|. The second specification does not include the eight economic variables discussed above. As
shown in the previous section, these variables vary across the two countries prior to the program and
ignoring them can lead to the rejection of the common trend assumption. Nevertheless, this does not
translate into significant differences in the parameter estimates between the second and third
specifications. The policy analysis in the next two sections uses parameter estimates from the third
specification.

    The first two coefficient estimates from the third specification suggest that the program has a
positive effect on the sales of the eligible vehicles and that the effect is stronger for vehicles that pass the
MPG requirement for the $3,500 rebate by a larger margin. This is likely due to the fact that the higher
the difference is, the more likely the vehicle is eligible for a $4,500 rebate. The next two coefficients
capture the effect of the program on ineligible vehicles during the program period. Given that the mean
of |∆GPM| is 0.64 with a minimum of 0.21 and a maximum of 2.14 for ineligible vehicles, this suggests
that the program reduces the sales of ineligible vehicles while the reduction is largest for vehicles that
barely miss the eligibility requirement. The results are consistent with expectations, as discussed in
Section 3.

     The fifth and sixth parameter estimates capture the program effect on eligible vehicles pre- and
post-program period. The coefficient estimates suggest that the program reduces the sales of eligible
vehicles and that the effect is stronger for eligible vehicles with higher MPG. The results from these two
parameter estimates and the first two are consistent with the intertemporal substitution that is
theoretically induced by the program. The seventh and eighth coefficient estimates suggest that the
program has almost no effect on the market share of ineligible vehicles at the average level of |∆GPM|,
although the effect becomes positive for vehicles that are farther away from the eligibility requirement.
As in the first specification, the parameter estimates in the third specification show that the primary
effect of the program in the pre- and post-periods is to reduce sales of eligible vehicles. This suggests
that the program affects vehicle sales mainly by changing purchase time rather than substitution from
ineligible vehicles to eligible ones.

     Table 5 also presents the estimates for the three parameters in the geometric function during the
three time periods. Figure 9 plots the geometric function over 100 days for each of the three time periods.
All of them exhibit a decaying pattern over time; the effect diminishes faster during the pre-program
period and slowest during the post-program period. This suggests an (intuitive) asymmetric response
when comparing before and after the program. A smaller effect is expected before the program officially

                                                      17
begins because fewer consumers were aware of the program and because of uncertainty about the
eligibility rules.

       Table 6 presents estimation results for specifications where the time effect is modeled using the
logistic function. The parameter estimates for the key variables of interest provide the same qualitative
findings as those from Table 5. Figure 10 plots the logistic function for each of the three periods. Similar
to the geometric function, the program effect diminishes fastest during the pre-program period and
slowest during the post-program period. Although the logistic function for the post-program period has a
larger curvature than the geometric function, the simulation results in the next section suggest that the
program effects on vehicles are robust to the two specifications.


4.3 Program Effect on New Vehicle Sales

Based on the parameter estimates from the third specification in Table 5 and 6, we simulate new vehicle
sales under the counterfactual scenario without the Cash for Clunkers program. Panel 1 of Table 7
reports U.S. monthly sales of new vehicles from June to December of 2009. Column (1) gives the
observed sales while columns (2) and (3) are the simulation results based on the specification where the
time effect is modeled using the geometric function. The results show that the program increased vehicle
sales in July and August while reducing the sales in other months.8

     The second and third panels in Table 7 show the program effect on the average MPG and GPM
(gallons per 100 miles) of the new vehicles for three time horizons: July-August, June-September, and
June-December. During July and August, the program increased the average MPG of new vehicles by
0.52 (from 22.84 to 22.37). Over a longer time horizon, the effect on average MPG diminished: although
the program increased sales of high MPG vehicles in July and August, it actually reduced sales of those
vehicles in other months. The next section demonstrates the importance of accounting for differences in
average MPGs under the two scenarios.

     Table 8 shows the program effects on vehicle sales for the industry and six major firms for three
time horizons. For the geometric decay function, sales during July and August were about 2.2 million
units while they would have been about 1.82 million in the absence of the program. The difference of
0.39 million is the sales induced by the program during the two months, compared to the roughly 0.66


8
 Because the program was in effect from July 27th-August 25th, the sales difference in July and August captures
the program effect during the program period as well as the intertemporal substitution in the days right before
or after the program within the month.
                                                      18
million new vehicles that participated in the program. This suggests that out of the 0.66 million program
participants, about 0.27 million would have purchased a new vehicle during July and August without the
program. This underscores that one cannot take the number of vehicles sold through the program as the
net program effect on vehicle sales.

     When taking June-September as the reference period, the program effect on vehicle sales decreases
to 0.31 million. This is due to the intertemporal substitution in June and September. The effect further
decreased to 0.246 million during the period from June to December. A similar pattern holds for
individual firms.
     Turning to the results for individual firms, Toyota saw the biggest increase in sales while Chrysler
saw the smallest in all three time horizons. The three Japanese firms accounted for the majority of the
sales increase because they offer more fuel-efficient models than the U.S.-based firms. The results based
on the logistic specification, as shown in columns (4) and (5), are very similar to those based on the
geometric function.


5. Program Effects on Gasoline Consumption and the Environment

This section evaluates the effectiveness of the policy in reducing motor gasoline consumption and CO2
emissions. To that end, we compare the observed outcomes (i.e., gasoline consumption and CO2
emissions) with the counterfactual outcomes in the absence of the program. In this section, we first
discuss our method and then present the results.


5.1 Method

The program affects gasoline consumption and pollution through two channels. First, the program
changes the fleet of new vehicles by causing some consumers to switch from fuel-inefficient vehicles to
fuel-efficient vehicles, and by causing other consumers to purchase a new vehicle when they would not
have otherwise. Second, it affects the fleet of used vehicles because the trade-in vehicles have to be
scrapped. A complete analysis of the two channels would involve an equilibrium model of the auto
market (including both new and used vehicles) that includes the dynamic effects of the program on both
channels in a unifying framework.

     Instead, we investigate the two channels based on the results from the previous section together
with some simplifying assumptions. The first assumption is that the scrappage of the trade-in vehicles

                                                   19
would not affect the remaining fleet of used vehicles. To the extent that the program would reduce the
availability of used vehicles in the second-hand market and hence increase used vehicle prices and
prolong their service, our analysis would over-estimate the energy and environmental benefits of the
program.

     The second assumption concerns the program effect on vehicle sales. Our previous analysis shows
that although the program results in an increase of about 0.26 million in new vehicle sales during June to
December of 2009, the effect of the program diminishes slowly and would still exist well beyond 2009
(see Figure 9). Nevertheless, the estimate of     % suggests     that the program effect on vehicle sales should
be negligible after 2012. Our simulations show that the effect of the program on sales in July and August
exceeded the June-December effect by 139,735 (i.e., due to decreased sales after the program). Based on
this decrease and the estimate of    %   in the geometric function, a back-of-the-envelope analysis suggests
that the program effect on sales would further decrease by 215,060 in total in the future. This implies
that the net increase in vehicle sales due to the program is 30,579 over the entire period that the program
would have an effect on the new vehicle market (about 3.5 years). The sales increase could come from
consumers who would not buy a new vehicle after selling or scrapping their used ones in the absence of
the program.

     The simulations based on the logistic specification provide similar results in that the program
would affect vehicle sales long after the program ended in August 2009. Nevertheless, the program
effect decays more slowly than with the geometric function. A back-of-the-envelope calculation based
on the estimate of   %   and the fact that the program reduced vehicle sales by 144,385 from September to
December, suggests that the program would reduce new vehicle sales by 162,931 during the first four
years after 2009. The increase sales of about 246,000 units due to the program during June to December
of 2009 would be exhausted eventually by year 13. The discrepancy in the long term effect from the two
specifications is likely driven by the functional form. Our following analysis assumes that the net
program effect on vehicle sales in the long run is 30,579 in one case and zero in the second case.

     Under the above two assumptions, the difference in gasoline consumption with and without the
program can be computed based on the difference between the following two quantities. The first is the
total gasoline consumption during the lifetime of the new vehicles sold from June to December 2009:

                                                   {J        H          H{                                   (7)




                                                        20
where J is the total sales of vehicles of model j during the period, and H             is the lifetime vehicle
miles of travel for model j. Lu (2006) estimates that the average lifetime VMT for passenger cars is
152,137 and that for light trucks is 179,954 based on the 2001 National Household Travel Survey.             H
is fuel consumption, which is measured in gallons per mile.

     The second quantity consists of three components of gasoline consumption: (1) by the trade-in
vehicles during their remaining lifetime in the absence of the program; (2) by the new vehicles that
would have been purchased from June to December of 2009; and (3) by the new vehicles that were
pushed forward into 2009 but would otherwise be sold after 2009 in the absence of the program:


                                    (#    H          H -       J     H          H -        
                                                                                             H         H    (8)

where     H     is the remaining VMT of the trade-in vehicle k. We estimate the remaining VMT of each
of the trade-in vehicles based on Lu (2006)’s estimates of age-specific survival probabilities as well as
estimated annual VMT for passenger cars and light trucks as shown in Table 9. With this information,
we predict age-specific remaining VMT for each type of vehicle, which is also shown in Table 9. Based
on this method, the average remaining VMT of trade-in vehicles is 59,716 with an average remaining
lifetime of 7 years.9

     The second term in equation (8) is the total lifetime gasoline consumption of new vehicles sold
from June to December in the absence of the program. J is the simulated sales of model j based on
estimation results in the previous section. The third term in equation (8) captures the difference in
gasoline consumption as a result of the difference in vehicles sold after 2009 between the two
scenarios.  is the effect of the program on vehicle sales after 2009. We assume that it is 245,639 in
one scenario and 215,060 in another, implying that the overall sales increase due to the program in the
long run is zero or 30,579 from our previous analysis.  and  are the average VMT and GPM of
                                                         H            H
these vehicles. We assume that these vehicles have the same characteristics as the new vehicles
purchased through the program. Because the average lifetime VMT is different for passenger cars and
light trucks, we estimate this term for the two vehicle types separately. The average GPM is 0.0367 for



9We compared the trade-in vehicles to the vehicles from the 2001 National Household Survey (NHTS), a
national survey on vehicle holdings and travel behavior. On average, the trade-in vehicles have higher mileage
than the vehicles with the same age from the 2001NHTS. The difference is larger for relatively new vehicles. So
our analysis could overestimate the remaining lifetime of the trade-in vehicles and the environmental benefit of
the program. Nevertheless, the majority of the trade-in vehicles are 10-20 years old and the average MPG of
these vehicles are quite close in these two data sets.
                                                       21
passenger cars and 0.0492 for light trucks. The share of passenger cars and light trucks is 0.152 and
0.848, respectively.


5.2 Results

Columns (1) and (2) in Table 10 present the total reductions in gasoline consumption and CO2 emissions
from the program for 12 cases. The total reductions are given by the differences in equations (7) and (8).
In cases 1-3 we assume that the program only shifts the purchase timing and does not increase new
vehicle sales in the long run. Case 1 shows that during the lifetime of the vehicles affected, the reduction
in total gasoline consumption is about 2,915 million gallons, which is about 8 days’ worth of current U.S.
gasoline consumption.
     Case 1 assumes that passenger cars have an average lifetime VMT of 152,137 and light trucks
179,954. However, more fuel efficient vehicles could have a higher VMT due to the lower fuel cost per
mile of travel, i.e., the rebound effect. Earlier studies often find a long-run rebound effect in the
neighborhood of 0.20-0.30 while a recent study by Small and van Dender (2007) shows that the rebound
effect could be declining largely due to income growth: their estimate of the rebound effect from 1966 to
2001 is 0.22 and that from 1997-2001 is 0.11. We incorporate the rebound effect of 0.1 and 0.5 in the
second and third cases.10 Because the vehicle fleet under the program is more fuel efficient than in the
absence of the program, a positive rebound effect would mean a higher total VMT under the program.
This would weaken the program effectiveness in reducing gasoline consumption. Therefore, the larger
the rebound effect, the smaller the reduction in total gasoline.

     The second panel presents results for cases where we assume that the net increase in new vehicles
sales due to the program is 30,579 units as suggested by the geometric specification for the time effect.
Since there would be more new vehicles on the road with the program than without, the total reductions
in gasoline consumption would be smaller than those in the first panel. For example, the total gasoline
reduction without the rebound effect is estimated at 2,659 million gallons in the second panel, compared
to 2,915 million gallons in the first panel.

      In calculating total gasoline consumption using equations (7) and (8), the first two panels in Table
10 apply the average lifetime VMT for new vehicles to both equations. This amounts to assuming that
the lifetime of the new vehicles sold from June to September coincides with that of the vehicles sold

10 The average MPG of passenger cars was 21.89 and that of light trucks was 17.45 in 2000. We use them as
the average MPGs corresponding to the lifetime VMT of 152,137 for passenger cars and 179,954 for light
trucks (2001 NHTS).
                                                  22
under the counterfactual scenario. However, some new vehicles that were bought during the program
period would have been purchased after 2009 in the absence of the program, e.g., due to the fact that
consumers would drive their trade-in vehicles longer. This implies that we should apply a smaller VMT
to some of the new vehicles in equation (8) because their lifetime does not coincide with that of the
vehicles sold during June to September of 2008. In panels 3 and 4, we reduce the VMTs for the new
vehicles under the counterfactual scenario in equation (8) so that the total VMT in equation (8) would be
the same as that in equation (7). This means that equation (8) now gives the total gasoline that will be
needed for the vehicles under the counterfactual scenario in order to travel the total lifetime VMT of
new vehicles sold from June to December of 2009. The numbers in panel 3 can be compared to those in
panel 1 while the numbers in panel 4 can be compared to those in panel 2. With the VMT reduction for
new vehicles in equation (8), the total reductions in gasoline consumption from the program are about
67 percent smaller in panel 3 and about 55 percent smaller in panel 4.

     For the reasons outlined above, the results in the first two panels likely provide the upper bound for
the true effect. We think that the results in the last two panels provide the lower bound. In the absence
of the program, there should be more vehicles in service due to the fact that the trade-in vehicles would
not be scrapped very quickly. Therefore, the total VMT of the whole fleet would likely be larger than the
smaller vehicle fleet with the program during the same time span (e.g., the lifetime of the vehicles sold
from June to December of 2009).

     Columns (3) to (6) present the dollar cost, from the perspective of government revenue, per unit
reduction in gasoline consumption and CO2 emissions. In calculating the unit cost, columns (3) and (4)
take into account the benefit of the program in reducing four criteria pollutants (carbon monoxide,
volatile organic compounds, nitrogen oxides, and exhaust particulates, i.e., CO, VOCs, NOx, and exhaust
PM2.5). The emissions of these pollutants per mile of travel for trade-in vehicles are from MOBILE6, a
computer program maintained by EPA that calculates emission factors for different types of vehicles.
The model takes into account the fact that as a vehicle ages, the emissions level per unit of travel can
increase dramatically, especially for older vehicles. To translate the reductions into monetary terms, we
assume that the average cost per ton of the four pollutants is $74.5, $180, $250, and $1,170, respectively.
The average cost for carbon monoxide is the average of the range reported by McCubbin and Delucchi
(1994). The other three cost parameters are the median marginal damage from Muller and Mendelsohn
(2009).



                                                    23
     Based on columns (3) and (4), the cost of reducing one gallon of gasoline consumption through the
program ranges from $0.89 to $2.92 while that of reducing one ton of CO2 ranges from $91 to $301.
Without taking into account the co-benefit of reducing criteria pollutants, the unit costs increase as
shown in columns (5) and (6): the range for the cost per gallon of reducing gasoline consumption
becomes $1.03 to $3.39 while that for CO2 reductions becomes $106 to $350.
     The implied cost of CO2 reduction from the program is far greater than projected market price
under several proposed legislative bills. For example, the allowance price for CO2 under the Waxman-
Markey cap-and-trade bill is projected to be $17-$22 per metric ton in 2020 in EPA’s analysis in 2020
and $28 in CBO’s analysis. This suggests that there are less costly alternatives in reducing CO2 to
achieve the level of reduction in the bill (i.e., 17 percent reduction from 2005 level by 2020). However,
since the Cash for Clunkers program also provides the benefit of stimulating the economy, it is perhaps
not fair to compare the implied carbon cost of the program to the allowance price in a national cap-and-
trade program.
     To put our results in perspective, we compare the cost-effectiveness of the program with two other
federal programs that use tax expenditure to reduce gasoline consumption and CO2 emissions. The first
is an excise tax credit of 51 cents per gallon of ethanol blended with gasoline (generally at a 10 percent
rate). Metcalf (2008) estimates that the cost of reducing gasoline consumption is about $2 per gallon and
that of reducing CO2 emissions is over $1,700 per ton in 2005. The second policy for comparison is the
income tax credit of up to $3,400 for hybrid vehicle purchases. Beresteanu and Li (2009) estimate that
the cost of reducing gasoline consumption is about $1.80 per gallon and the cost of reducing CO2
emissions is $177 per ton. The unit cost estimates of reducing gasoline consumption for both programs
are comparable to the cost of the Cash for Clunkers program. For reducing CO2 emissions, the tax credit
for ethanol is clearly dominated by the other two programs.


6. Program Effect on Employment

In this section, we explore the effects of the program on production worker employment at vehicle parts
and assembly plants, over two different time horizons: a short term effect from June to December 2009,
and a long term effect from June 2009 to May 2010. Because many of the incremental sales under the
program likely came out of inventories, we extend the short term effect to include the remaining months
of the calendar year. Because of data limitations, we do not analyze the impact of the program on other
occupations or industries, although the program may have in fact affected other sectors of the economy.


                                                   24
     The analysis is based on two assumptions. First, over the time horizons considered, the program
had zero net effect on dealer inventories. That is, actual inventories of each vehicle model at the end of
each period are exactly equal to counterfactual inventories. In that case, the estimated effect of the
program on sales is exactly equal to the effect on vehicle production.

     The second assumption is that the program did not affect the relationship between vehicle
production and employment. Under these two assumptions, the estimated relationship between
employment and production from before the program can be used to estimate counterfactual
employment during and after the program. We now describe the estimation procedure in more detail.

     As discussed above, we use employment and production data from the BLS and FRB. Figure 11
plots monthly production and worker hours. The data series are very highly correlated at a monthly
frequency, and the overall time trends are similar. These variables are used to estimate the following
equation:

                                  H          -           -   -     -                         (9)

     The sample includes observations from March 2006 through May 2009. The dependent variable is
total production worker hours at motor vehicle assembly plants. The independent variables include the
monthly seasonally adjusted production volume, as well as a set of month and year dummies (we use
seasonally adjusted production because the short sample prevents us from reliably estimating the
seasonal effects). The coefficient    represents the change in assembly plant production worker hours
associated with a marginal change in production.

     A similar equation is estimated for production worker hours at parts plants in the United States.
Note that we use data on U.S. production, although employment at U.S. parts plants may also depend on
vehicle production in Canada and Mexico. The coefficient on production volume,          , is interpreted as
the change in parts employment hours for a marginal change in vehicle production.

        and     are the key parameters needed to estimate the effect of the program on employment. The
parameters represent the average effects of production on hours over the sample period. The
relationships reflect underlying changes at individual parts and assembly plants, which we assume are
similar during the sample period and during the time period of June - December 2009. Note that total
production was relatively depressed in the second half of 2009. Therefore, if     varies with production,
the estimated    would be different from the true value during the second half of 2009 (and similarly for
  ). Unfortunately, data for production worker hours are not available prior to 2006, which prevents us

                                                    25
from testing the stability of     over time. Consequently, we maintain the hypothesis that the program
did not affect the coefficients. The estimate of       is 23.69 (heteroskedasticity robust standard error 4.24)
and the estimate of     is 25.56 (robust standard error 7.03). Both regressions have 39 observations and
the R-squared values are 0.97 and 0.99. The results are similar if lags of production are added, and there
is no evidence that serial correlation significantly affects the results (e.g., the coefficients are similar if
the lagged dependent variable is added to either regression).

     We estimate the program effect on employment by combining the estimated relationships between
production and employment with the estimated effect of the program on individual model sales. It is
necessary to account for the fact that many of the vehicles sold in the program were imported, and thus
did not significantly affect employment at parts or assembly plants in the United States. For each vehicle
model sold under the program, we calculate the share of vehicles assembled in the United States,              .
The effect of the program on hours, H , is calculated as:

                                          H        J              {    -    {                             (10)

where J is the estimated effect of the program on sales (and, hence, production) of model j from June to
December; and       is the coefficient on production in the parts regression. For each vehicle model, the
change in assembly worker hours is equal to the estimated change in production of the model, J ,
multiplied by the share of production in the U.S., and the effect of production on assembly hours,            ;
worker hours for the parts industry are calculated similarly. The production share in the US is calculated
based on 2007-2009 data from Wards. The estimated change in hours is equal to the sum over vehicles
of the change in estimated assembly and parts worker hours. Finally, hours are converted to full-time job
equivalents, using average weekly hours.

     Table 11 reports the employment estimates. The estimated short run (June – December 2009)
effect of the program on total employment is 3,676 job-years using the geometric decay function, and is
roughly split between the assembly and parts industries. For comparison, the estimated sales effect is
246,000 vehicles, which implies that approximately one job-year was created for every 67 vehicles sold
under the program. The long run effect, over June 2009-May 2010, is approximately half the short run
effect, or 2,050 job-years. The results are similar using the logistic decay function.

     The employment effect is smaller than, though broadly similar to, the employment estimate in
CEA, which is the most directly comparable to this study. CEA estimates that about 4,300 assembly job-


                                                        26
years were created in 2009, which is based on a similar estimate of production and a smaller estimate of
job-years per vehicle.

     In contrast, NHTSA estimates that 38,600 jobs were created in the parts and assembly plants. Two
factors may explain this discrepancy: first, NHTSA estimates that the program increased production by
almost 600,000 vehicles, and second, NHTSA estimates one job-year per 15.5 vehicles produced. Note
that the production estimate is based on survey responses from program participants and does not
account for imports. Furthermore, the employment-production relationship uses a different industry
classification from this paper.

     Finally Cooper et al. estimate that 29,100 job-years were created. That estimate includes jobs
associated with intermediate inputs to assembly and parts plants, in addition to employment associated
with the increase in household purchases, and is not directly comparable to the estimates in this paper.


7. Conclusion

As part of the stimulus effort, the Cash for Clunkers program was so popular that it exhausted its
originally allocated $1 billion within one week despite initial projections that the program period would
be three months. Nevertheless, while many considered the program to be a great success as a short-term
stimulus measure, critics argued that the increased sales observed during the program period could be
merely borrowed from immediate future months so that even the short-term effect on vehicle sales may
not have been significant. Many have also raised doubts over the potential impact of the program on
energy consumption and the environment.

     Using a difference-in-differences approach with Canada as the control group, we have examined
program effects on vehicle sales in different time-horizons as well as its impacts on pollutant emissions,
gasoline consumption, and employment. Our analysis offers mixed evidence on the overall performance
of the program. We find that although a large portion of vehicles sold under the program was a result of
demand switching from months surrounding the program, 0.24 million vehicles (out of 0.68 million)
would not have been sold during 2009 without the program. This means that a significant number of
vehicles sold under the program were pulled forward from after 2009. Therefore, the program indeed
provided some short-term stimulus to the auto market. However, if the program were to be judged as an
environmental program, the implied costs of reducing gasoline consumption and CO2 emissions are
quite high: the best case scenario suggests a cost of over $91 in government revenue for each ton of CO2
avoided and almost 90 cents for each gallon of gasoline consumption. In terms of the program effect on
                                                    27
employment, we estimate that 3,676 job–years were created during June-December of 2009 in auto
assembly and parts industries due to the program, and the effect decreased to 2,050 job years over June
2009 – May 2010.

     What can we learn from the program? The program did increase sales, reduce gasoline
consumption and emissions, and increase employment. However, the contrast between the effect on
vehicle sales and that on the environment perhaps speaks to the inherent conflict of the two goals. In the
context of the purchase of new vehicles and the scrappage of the used vehicles, one can instead
conjecture two parallel programs, with each targeting one of the two goals. The first one, aiming to
provide stimulus to the economy, would provide a rebate on new vehicle purchases based on the
ownership of used vehicles much as in the Cash for Clunkers program. Nevertheless, it would not
require the used vehicle to be turned-in or dismantled. Eliminating that requirement would make it more
likely to pull sales forwards from further in the future. The second program, aiming to reduce old gas
guzzlers on the road, would provide a separate rebate to consumers who recycle their old, fuel-
inefficient vehicles. The environmental program would provide greater incentives for improving fuel
economy than under Cash for Clunkers. These two programs would have a broader participation than the
Cash for Clunkers program and would likely be more effective in achieving the two goals
simultaneously.




                                                   28
References:

Abrams, Burton and George Parsons, “Is Cars a Clunker?” The Economist’s Voice, August 2009.
Beresteanu, Arie, and Shanjun Li, “Gasoline Prices, Government Support, and the Demand for Hybrid
   Vehicles in the U.S.,” International Economic Review, forthcoming.
Berry, Steven, “Estimating Discrete Choice Models of Product Differentiation,” Rand Journal of
   Economics, 25 (1994), 242-262.
Bram, Jason and Sydney C. Ludvigson, “Does Consumer Confidence Forecast Household Expenditure?
   A Sentiment Index Horse Race,” Federal Reserve Bank of New York: Economic Policy Review. 4:2
   (1998), 59–78.
Carroll, Christopher D., Jeffrey C. Fuhrer and David W. Wilcox, “Does Consumer Sentiment Forecast
   Household Spending? If So Why?” American Economic Review, 84:5 (1994),1397–1408.
Cooper, Adam, Yen Chen and Sean McAlinden. “CAR Research Memorandum: The Economic and
   Fiscal Contributions of the ‘Cash for Clunkers’ Program – National and State Effects.” Center for
   Automotive Research (2010).
Council of Economic Advisors. “Economic Analysis of the Car Allowance Rebate System (‘Cash for
   Clunkers’).” Executive Office of the President of the United States (2009).
Eissa, Nada, and Jeffrey Liebman, “Labor Supply Response to the Earned Income Tax Credit,”
   Quarterly Journal of Economics, 111:2 (1996), 605-637.
Galiani, Sebastian, Paul Gertler, and Ernesto Schargrodsky, “Water for Life: The Impact of the
   Privatization of Water Services on Child Mortality”, Journal of Political Economy, 113:1(2005), 83-
   119.
Knittel, Christopher, “The Implied Cost of Carbon Dioxide under the Cash for Clunkers Program,”
   University of California-Davis Working Paper, 2009.
Lu, S, “Vehicle Scrappage and Travel Mileage Schedules,” National Highway Traffic Safety
   Administration Technical Report, January 2006.
Ludvigson, Sydney, “Consumer Confidence and Consumer Spending,” Journal of Economic
   Perspectives, 18:2 (2004), 29-50.
McCubbin, Donald and Mark Delucchi, “The Health Costs of Motor-Vehicle Related Air Pollution,”
   Journal of Transportation Economics and Policy, 33(1999), 253-286.
Metcalf, Gilbert, “Using Tax Expenditures to Achieve Energy Policy Goals,” American Economic
   Review Papers and Proceedings, 98(2008), 90-94.


                                                  29
Muller, Nick and Robert Mendelsohn, “Efficient Pollution Regulation: Getting the Prices Right,”
   American Economic Review, 99 (2009), 1714-1739.
National Highway Traffic Safety Administration. “Consumer Assistance to Recycle and Save Act of
   2009: Report to Congress.” US Department of Transportation, December 2009.
Small, Kenneth and Kurt van Dender, “Fuel Efficiency and Motor Vehicle Travel: The Declining
   Rebound Effect,” Energy Journal, 28(2007), 25-51.




                                               30
                                    Figure 2: Monthly New Vehicle Sales in U.S. and Canada from 2007 to 2009


                              15


                              14

                                                                      US Sales
                              13
                                                                      CA Sales
                                                                                                      CARS




               Log(Sales)
                              12


                              11
                               01/2007    06/2007      12/2007       06/2008      12/2008       06/2009        12/2009



                               1

                             0.5

                               0

                             -0.5

                              -1                                     US Sales
                                                                     CA Sales
                             -1.5                                                                     CARS




Demeaned Sales/1000 people
                              -2
                               01/2007    06/2007      12/2007       06/2008      12/2008       06/2009        12/2009



           Note: The top graph shows the total monthly sales in logarithm. The bottom graph plots monthly
           sales per 1,000 people after demeaning using the 2007-2008 monthly averages.

                                                                      31
                                    Figure 3: Monthly Eligible Vehicle Sales in U.S. and Canada from 2007 to 2009


                              15


                              14


                              13                                     Eligible US
                                                                     Eligible CA




               Log(Sales)
                                                                                                         CARS
                              12


                              11
                               01/2007      06/2007      12/2007       06/2008       12/2008       06/2009          12/2009



                               1

                             0.5

                               0

                             -0.5

                              -1                                      Eligible US
                                                                      Eligible CA
                             -1.5                                                                       CARS




Demeaned Sales/1000 people
                              -2
                               01/2007      06/2007      12/2007       06/2008       12/2008       06/2009          12/2009



              Note: The top graph shows the total monthly sales for eligible vehicles in logarithm. The bottom
              graph plots monthly sales per 1,000 people after demeaning using the 2007-2008 monthly averages.

                                                                          32
                                 Figure 4: Monthly Ineligible Vehicle Sales in U.S. and Canada from 2007 to 2009


                               13

                               12

                               11                                    Ineligible US
                                                                     Ineligible CA
                                                                                                        CARS
                               10




                Log(Sales)
                                9

                                8
                                01/2007    06/2007      12/2007      06/2008            12/2008   06/2009      12/2009



                              0.2

                              0.1

                                0
                                                                        Ineligible US
                              -0.1                                      Ineligible CA

                              -0.2                                                                      CARS




 Demeaned Sales/1000 people
                              -0.3
                                 01/2007   06/2007      12/2007      06/2008            12/2008   06/2009      12/2009



Note: The top graph shows the total monthly sales for ineligible vehicles in logarithm. The bottom
graph plots monthly sales per 1,000 people after demeaning using the 2007-2008 monthly averages.

                                                                       33
                            Figure 5: Monthly Gasoline Price in U.S. and Canada from 2007 to 2009

               5.5

                                                                                           US Gas Price
                5                                                                          CA Gas Price


               4.5


                4


               3.5




Price in US$
                3


               2.5


                2


               1.5
                  01/2007     06/2007        12/2007        06/2008       12/2008        06/2009          12/2009




                                                             34
                             Figure 6: Monthly Interest Rate in U.S. and Canada from 2007 to 2009

                  9

                                                                                                US Interest Rate
                  8                                                                             CA Interest Rate



                  7



                  6




Interest Rate %
                  5



                  4



                  3



                  2
                   01/2007    06/2007        12/2007        06/2008        12/2008        06/2009           12/2009




                                                             35
           Figure 7: Consumer Confidence Index in U.S. and Canada from 2007 to 2009

12
                                                                     US Consumer Confidence Index
11                                                                   CA Consumer Confidence Index


10

9


8

7


6

5


4

3


2
 01/2007       06/2007       12/2007        06/2008        12/2008          06/2009           12/2009




                                              36
             Figure 8: Monthly Vehicle Sales (Controlling for Demand Factors) in U.S. and Canada


             16

             15

             14             Eligible US
                            Eligible CA




Log(Sales)
             13


             12
              01/2007      06/2007           12/2007        06/2008          12/2008        05/2009


             15

             14

             13

             12              Ineligible US




Log(Sales)
                             Ineligible CA
             11

             10
              01/2007      06/2007           12/2007        06/2008          12/2008        05/2009


Note: The top graph shows the total month sales (in log) of predicted sales of eligible vehicles after
removing the effect of observed demand factors (e.g., gas price, interest rate, consumer confidence
and seasonality). The bottom graph plots the total month sales (in log) of predicted sales of
ineligible vehicles after removing the effect of observed demand factors.

                                                       37
                    Figure 9: Time Effect during Three Periods Using Geometric Function


             1


            0.5




Geometric
             0
              0    10     20      30       40        50      60     70      80      90    100
                                                Program days
             1


            0.5




Geometric
             0
              0    10     20      30       40       50      60      70      80      90    100

                                            Pre-program days
             1

            0.8

            0.6




Geometric
            0.4
               0   10     20      30       40       50      60      70      80      90    100
                                            Post-program days




                                                     38
              Figure 10: Time Effect during Three Periods Using Logistic Function


         1


        0.5




Logit
         0
          0   10      20       30      40        50      60      70       80        90   100
                                            Program days
         1


        0.5




Logit
         0
          0   10      20       30      40      50       60       70       80        90   100
                                        Pre-program days
         1


        0.5




Logit
         0
          0   10      20       30      40       50      60       70       80        90   100
                                        Post-program days




                                               39
                        Figure 11: Monthly Production Worker Hours


          Monthly Assemblies, Assemblies Production Worker Hours
         and Parts Production Worker Hours, 2006-2010 (BLS and FRB)
120,000,000                                                                                   1,000,000
                                                                                              900,000
100,000,000
                                                                                              800,000
                                                                                              700,000
 80,000,000
                                                                                              600,000
 60,000,000                                                                                   500,000
                                                                                              400,000
 40,000,000
                                                                                              300,000
                                                                                              200,000
 20,000,000
                                                                                              100,000
         0                                                                                    0
       12/14/2005 10/10/2006    8/6/2007     6/1/2008    3/28/2009   1/22/2010 11/18/2010


                 Assemblies Hours          Parts Hours       Production Volume (right axis)




                                               40
                                Table 1A: Rebate Eligibility Requirements


                                         Eligibility Requirements

                            •    Is in drivable condition
                            •    Has been both continuously insured, consistent with the laws of your State,
                                 and continuously registered to the same owner for at least one year
                                 immediately prior to the trading-in of your vehicle under the CARS program
    Trade-in Vehicle        •    Manufactured less than 25 years before the date of trade (i.e., before mid- to
                                 late- 1984) and, in the case of category 3 trucks, not later than model year
                                 2001
                            •    Has a combined MPG of 18 or less (this does not apply to category 3 trucks,
                                 i.e., very large pickup trucks and cargo vans)
New Vehicle (Purchased or   •    Is new (i.e., legal title has not been transferred to anyone)
        Leased)             •    Has manufacturer’s suggested retail price of $45,000 or less




                                                      41
                                               Table 1B: Rebate Amounts

                                                    Incentive Amounts

                                                 The                                          Amount of Incentive
                                               combined           The type of
                                                                                       If the difference in
  If the type of new vehicle you want is…     MPG* of the     vehicle you trade-                                      The
                                                                                     combined MPG between
                                              new vehicle       in must be a…                                      incentive
                                                                                     new vehicle and trade-in
                                               must be…                                                               is…
                                                                                           vehicle is…
 Passenger Automobile                                              Passenger car,            4-9 MPG              3500
                                               At least 22
    • All passenger cars                                           category 1 or
                                                 MPG                                     10 MPG or more                   4500
                                                                  category 2 truck
 Category 1 Truck†
     • All SUVs w/ GVWR <= 10,000 lbs                                                        2-5 MPG              3500
     • All pickups w/ GVWR < 8,500 lbs                           Passenger car,
                                                 At least 18
         & wheelbase <= 115 inches                               category 1 or
                                                   MPG
     • Passenger vans and cargo vans w/                         category 2 truck
                                                                                         5 MPG or more                    4500
         GVWR < 8,500 lbs and wheelbase
         <= 124 inches
 Category 2 Truck†                                                                            1 MPG               3,500
     • Pickups w/ GVWR <= 8,500 lbs &                           Category 2 truck
         wheelbase > 115 inches                  At least 15                             2 MPG or more                    4,500
     • Passenger vans and cargo vans w/            MPG
         GVWR <= 8,500 lbs and                                                                 NA‡
                                                                Category 3 truck                                  3,500
         wheelbase > 124 inches
 Category 3 Truck†                                                                             NA‡
     • Trucks w/ GVWR 8,500 – 10,000                                                 However, the new vehicle
         lbs that are either pickup trucks          NA‡         Category 3 truck                                  3,500
                                                                                     must be similar in size or
         with cargo beds 72” or longer or
                                                                                     smaller than the trade-in
         very large cargo vans
* MPG requirements are based on EPA’s combined city/highway rating
† GVWR = Gross Vehicle Weight Rating
‡ Not applicable: Category 3 trucks do not have EPA MPG ratings



                                                             42
                    Table 2: Summary Statistics of Sales Data and Economic Variables
Panel 1: New Vehicles
                                     No. of Observations              Monthly Sales per Model
                               Eligible        Ineligible  All   Eligible Ineligible       All
U.S.                             6,394           2,742     9,136   5,254      1,878       4,241
Canada                           5,476           2,202     7,678    774        157         597
                                       Average Vehicle Price              Average MPG
                               Eligible        Ineligible    All Eligible Ineligible       All
U.S.                            24,780          43,678    30,452 23.28        18.01       21.70
Canada                          24,071          42,920    29,477 22.62        17.96       21.28



Panel 2: Demand Factors
                                         Gasoline Price        Interest Rate           Confidence Index
                                     Mean             S.D.     Mean        S.D.       Mean         S.D.
 U.S.                                 2.74            0.56      4.80       1.33       78.03       28.93
 Canada                               3.54            0.65      6.61       0.64       91.43       18.17
Note: Panel 1 gives statistics for variables at the month-model level for years from 2007 to 2009 while the
variables in panel 2 are for 36 months during the three year period. The interest rate for U.S. is the
monthly average of new car loans at auto finance companies while that for Canada is the monthly five-
year personal mortgage rate. The consumer confidence index for U.S. is from the Conference Board
consumer confidence survey while that for Canada is by the Conference Board of Canada.




                                                    43
            Table 3: Trade-in and New Vehicles Participating in the Program
                                       Cars                   Trucks               All
                                 Mean        S.D.        Mean       S.D.     Mean        S.D.
Panel 1: Trade-in Vehicles
MPG                               17.55      1.01        15.50       1.75    15.81       1.81
Age                               15.60      4.20        13.45       3.99    13.78       4.10
VMT                            140,833 53,940 150,432 53,284 148,982 53,494
Observations                     99,624                559,776             659,400
Panel 2: New Vehicles
MPG                               27.96      5.21        20.73       3.17    25.00       5.73
Rebate ($)                        4,224       451        4,200       462     4,214        456
Observations                   388,809                  270,591            659,400
Note: There are 678,359 transactions made under the program based on the public database
provided at www.cars.gov. In order to be consistent with our analysis of the new vehicle
market, we delete 18,959 transactions, which including 2,278 category 3 new vehicles, 6,169
leasing, and the remaining due to data errors (e.g., out of range MPG data). The total rebate
amount for these 659,400 transactions is about $2.78 billion, comparing to a total program
payment of $2.85 billion.




                                             44
                                        Table 4: Testing Common Trend
                                        Specification 1            Specification 2   Specification 3   Specification 4
Variable                                Para     S.E.              Para     S.E.      Para    S.E.      Para S.E.
U.S. dummy *Elig dummy* 02/09 dummy     0.018 0.055               -0.078 0.063       0.002 0.071       0.095 0.119
U.S .dummy * Elig dummy * 03/09 dummy  -0.243 0.050               -0.267 0.063       -0.101 0.066      -0.024 0.108
U.S. dummy *Elig dummy * 04/09 dummy   -0.377 0.054               -0.366 0.066       -0.057 0.068      0.074 0.133
U.S. dummy *Elig dummy * 05/09 dummy   -0.308 0.060               -0.360 0.069       -0.136 0.071      0.061 0.169
U.S. dummy *Inelig dummy * 02/09 dummy -0.122 0.064               -0.207 0.071       -0.045 0.107      0.047 0.143
U.S. dummy *Inelig dummy * 03/09 dummy 0.043 0.052                -0.015 0.064       -0.088 0.096      -0.044 0.129
U.S. dummy *Inelig dummy * 04/09 dummy 0.003 0.054                -0.054 0.064       -0.030 0.094      0.059 0.147
U.S. dummy *Inelig dummy * 05/09 dummy 0.078 0.055                -0.006 0.062       -0.161 0.098      0.018 0.178
Month gas price (p1)                    0.733 0.038               0.716 0.042        -0.093 0.089      -0.189 0.096
Quarter gas price (p2)                 -0.271 0.057               -0.183 0.062       -0.345 0.175      -0.263 0.234
DPM1 (p1/MPG)                          -9.918 0.750               -9.974 0.824       -4.953 1.093      -3.963 1.155
DPM2 (p2/MPG)                           0.503 1.131               -0.135 1.249       5.484 2.757       4.230 2.844
 Country-product fixed effects (1433)              Yes              Yes                 Yes              Yes
 Economic variables (8)                            No               Yes                 No               Yes
 More fixed effects (70)                           No                No                 Yes              Yes
 R-squared                                       0.9612            0.9616             0.9655           0.9657
Note: These are estimation results for equation (6). The dependent variable is the logarithm of vehicle sales. The
number of observations is 13,524. Elig dummy is the dummy variable for eligibility. 02/09 dummy is the dummy
variable for February 2009. Month gas price is the average regular gasoline price in the current month while quarter
gas price is the average gasoline price in the 3 months before the current month. A model is defined as a country-
vintage-nameplate combination in a given year. Economic variables (8) include the monthly interest rate, monthly
consumer confidence index, their interactions with log(vehicle price), as well as the interactions of U.S. dummy with
these four variables. More fixed effects include year-month dummies (26), month dummies (11) interacting with car
dummy, month dummies interacting with MPG, and the interactions of previous 22 variables with U.S. dummy.


                                                         45
                              Table 5: DID Results with Geometric Growth Function
                                                          Specification 1    Specification 2    Specification 3
Variable                                                   Para       S.E.    Para       S.E.    Para        S.E.
Elig dummy* effective program days                         0.077     0.028    0.013     0.011    0.014      0.011
Elig dummy * |∆GPM| * effective program days                No        No      0.052     0.014    0.051      0.014
Inelig dummy* effective program days                      -0.049     0.020   -0.043     0.016   -0.043      0.016
Inelig dummy * |∆GPM| * effective program days              No        No      0.013     0.015    0.015      0.015
Elig dummy* effective pre/post- days                      -0.008     0.004   -0.003     0.002   -0.001      0.003
Elig dummy* |∆GPM| * effective pre/post- days               No        No     -0.002     0.002   -0.002      0.002
Inelig dummy* effective pre/post-days                      0.002     0.003   -0.007     0.003   -0.005      0.003
Inelig dummy * |∆GPM| * effective pre/post- days            No        No      0.013     0.004    0.013      0.003
Month gas price (p1)                                       0.025     0.092   -0.063     0.085   -0.008      0.089
Quarter gas price (p2)                                    -0.773     0.208   -0.522     0.163   -0.679      0.207
DPM1 (p1/MPG)                                             -6.795     1.203   -5.475     1.094   -6.665      1.183
DPM2 (p2/MPG)                                             11.868     2.695    8.434     2.566    9.487      2.665
 # (geometric growth during program)                       0.286     0.081    0.399     0.080    0.405      0.079
 $ (geometric growth pre-program)                          0.923     0.307    0.325     0.356    0.207      0.404
 % (geometric growth post-program)                         0.819     0.129    0.945     0.038    0.960      0.037
Product fixed effects (1436)                                Yes                Yes                Yes
Economic variables (8)                                      Yes                No                 Yes
More fixed effects (70)                                     Yes                Yes                Yes
J-statistics                                               6.125             11.868             13.862
Note: These are estimation results for equations (1) and (5) using two-step GMM method. The dependent variable is
the logarithm of vehicle sales The number of observation is 16,814. Effective program days and effective pre-/post-
days are defined using geometric growth function according to equations (2)-(4). |∆GPM| is the absolute difference
between the GPM of the vehicle and the eligibility requirement.




                                                        46
                                Table 6: DID Results with Logistic Growth Function
                                                                  Specification 1   Specification 2 Specification 3
Variable                                                          Para       S.E.  Para       S.E.        Para    S.E.
Elig dummy* effective program days                                0.134     0.044 0.025      0.020       0.025 0.021
Elig dummy * |∆GPM| * effective program days                       No        No    0.097     0.026       0.095 0.025
Inelig dummy* effective program days                             -0.087     0.033 -0.081     0.029       -0.081 0.030
Inelig dummy * |∆GPM| * effective program days                     No        No    0.024     0.029       0.029 0.028
Elig dummy* effective pre/post- days                             -0.014     0.006 -0.006     0.004       -0.002 0.005
Elig dummy* |∆GPM| * effective pre/post- days                      No        No   -0.005     0.004       -0.005 0.004
Inelig dummy* effective pre/post-days                            0.003      0.006 -0.014     0.006       -0.010 0.006
Inelig dummy * |∆GPM| * effective pre/post- days                   No        No    0.026     0.006       0.025 0.006
Month gas price (p1)                                              0.024     0.092 -0.063     0.085       -0.008 0.089
Quarter gas price (p2)                                           -0.771     0.208 -0.521     0.163       -0.678 0.207
DPM1 (p1/MPG)                                                    -6.795     1.203 -5.475     1.093       -6.665 1.183
DPM2 (p2/MPG)                                                    11.879     2.695 8.430      2.566       9.487 2.666
  # (logistic growth during program)                              1.578     0.308 1.225      0.230       1.211 0.225
  $ (logistic growth pre-program)                                 0.091     0.561 1.614      1.492       2.203 2.633
  % (logistic growth post-program)                                0.264     0.174 0.090      0.055       0.071 0.056
Product fixed effects (1436)                                       Yes              Yes                   Yes
Economic variables (8)                                             Yes              No                    Yes
More fixed effects (70)                                            Yes              Yes                   Yes
J-statistics                                                      6.157           11.909                 13.866
Note: These are estimation results for equations (1) and (5) using two-step GMM method. The number of observation is
16,814. Effective program days and effective pre-/post-days are defined using logistic growth function according to
equations (2)-(4). |∆GPM| is the absolute difference between the GPM of the vehicle and the eligibility requirement.




                                                          47
      Table 7: New Vehicle Sales June- December 2009 in the U.S. under Two Scenarios
                                             Geometric Function          Logistic Function
                          Observed     Counterfactual Difference      Counterfactual Difference
                                  (1)             (2)         (3)                 (4)        (5)
Pane 1: Effect on Vehicle Sales
June                        828,286               828,395      -109          828,321          -35
July                        970,490               840,858   129,632          841,363      129,127
August                    1,231,137               975,286   255,851          976,060      255,077
September                   719,795               756,421   -36,626          757,724      -37,929
October                     810,066               848,605   -38,539          850,106      -40,040
November                    719,140               748,067   -28,927          748,967      -29,827
December                    992,053             1,027,696   -35,643        1,028,143      -36,090
Panel 2: Effect on Vehicle MPG
July-August                    23.37                22.84      0.52            22.84         0.52
June-September                 23.03                22.74      0.29            22.74         0.29
June-December                  22.75                22.62      0.13            22.62         0.13
Panel 3: Effect on Vehicle gallons per 100 miles (GPM)
July-August                  4.47             4.56        -0.09               4.56           -0.09
June-September               4.53             4.58        -0.05               4.58           -0.05
June-December                4.59             4.61        -0.02               4.61           -0.02
Note: Counterfactual scenario refers to the case without the Cash for Clunkers program. The
counterfactual sales are simulated based on GMM parameter estimates for the third specification in
Tables 5 and 6.




                                                     48
             Table 8: Program Effects on Sales for the Industry and Automakers
                                       Geometric Function          Logistic Function
                     Observed Counterfactual Difference         Counterfactual Difference
                             (1)                  (2)       (3)             (4)          (5)
Panel 1: Effects during July and August 2009
Industry              2,201,627            1,816,144   385,483       1,817,423      384,204
GM                      405,394              337,025    68,369         337,262       68,132
Ford                    318,573              269,153    49,420         269,343       49,230
Chrysler                181,846              161,858    19,988         161,971       19,875
Toyota                  402,317              309,959    92,358         310,177       92,140
Honda                   276,003              215,044    60,959         215,194       60,809
Nissan                  176,931              141,590    35,341         141,691       35,240
Panel 2: Effects during June to September 2009
Industry              4,559,774            4,249,565   310,209       4,253,574      306,200
GM                      865,478              810,380    55,098         811,141       54,337
Ford                    684,092              645,376    38,716         645,971       38,121
Chrysler                373,874              359,780    14,094         360,096       13,778
Toyota                  812,332              738,558    73,774         739,335       72,997
Honda                   539,012              489,399    49,613         489,855       49,157
Nissan                  350,359              320,424    29,935         320,732       29,627
Panel 3: Effects during June to December 2009
Industry              6,270,967            6,025,328   245,639       6,030,684      240,283
GM                    1,189,728            1,145,874    43,854       1,146,890       42,838
Ford                    963,950              935,454    28,496         936,275       27,675
Chrysler                511,564              502,412     9,152         502,827        8,737
Toyota                1,130,300            1,072,529    57,771       1,073,544       56,756
Honda                   720,035              680,018    40,017         680,588       39,447
Nissan                  479,840              454,393    25,447         454,811       25,029

                                            49
    Table 9: Remaining Lifetime VMT for Cars and Light Trucks
Age   Survival Probability     Annual VMT         Remaining VMT
         Cars      Trucks     Cars    Trucks      Cars      Trucks
1      0.9900       0.9741   14231     16085    152143      179957
2      0.9831       0.9603   13961     15782    139449      168657
3      0.9731       0.9420   13669     15442    126467      155299
4      0.9593       0.9190   13357     15069    114097      142874
5      0.9413       0.8913   13028     14667    102382      131380
6      0.9188       0.8590   12683     14239     91312      120796
7      0.8918       0.8226   12325     13790     80865      111100
8      0.8604       0.7827   11956     13323     70988      102226
9      0.8252       0.7401   11578     12844     61623       94114
10     0.7866       0.6956   11193     12356     52673       86687
11     0.7170       0.6501   10804     11863     44065       79877
12     0.6125       0.6040   10413     11369     37538       73604
13     0.5094       0.5517   10022     10879     33530       67853
14     0.4142       0.5009    9633     10396     30294       63406
15     0.3308       0.4522    9249      9924     27624       59441
16     0.2604       0.4062    8871      9468     25339       55918
17     0.2028       0.3633    8502      9032     23319       52783
18     0.1565       0.3236    8144      8619     21440       49984
19     0.1200       0.2873    7799      8234     19639       47497
20     0.0916       0.2542    7469      7881     17813       45264
21     0.0696       0.2244    7157      7565     15867       43277
22     0.0527       0.1975    6866      7288     13726       41459
23     0.0399       0.1735    6596      7055     11262       39818
24     0.0301       0.1522    6350      6871      8278       38271
25     0.0227       0.1332    6131      6739      4624       36756
26          0       0.1165       0      6663          0      35259
27                  0.1017              6648                 33651
28                  0.0887              6648                 31900
29                  0.0773              6648                 29927
30                  0.0673              6648                 27693
31                  0.0586              6648                 25160
32                  0.0509              6648                 22247
33                  0.0443              6648                 18964
34                  0.0385              6648                 15142
35                  0.0334              6648                 10775
36                  0.0290              6648                  5772

                                50
                                         Table 10: Cost-Effectiveness Analysis
                                               Total Reductions       Cost ($) w/ Co-benefit Cost ($)w/o Co-benefit
                                              Gasoline       CO2        Gasoline     CO2      Gasoline      CO2
                                             (mil gallons) (mil tons) (per gallon) (per ton) (per gallon) (per ton)
                                                   (1)        (2)          (3)        (4)         (5)        (6)
Panel 1: No Increase in Vehicle Sales
Case 1: No rebound effect                       2914.67       28.27           0.89        91.45        1.03        106.11
Case 2: Rebound elasticity = 0.1                2883.38       27.97           0.90        92.44        1.04        107.26
Case 3: Rebound elasticity = 0.5                2758.22       26.75           0.94        96.63        1.09        112.13
Panel 2: Increase in Vehicle Sales
Case 4: No rebound effect                       2658.58       25.79           0.97       100.26        1.13        116.33
Case 5: Rebound elasticity = 0.1                2622.24       25.44           0.99       101.64        1.14        117.94
Case 6: Rebound elasticity = 0.5                2476.88       24.03           1.04       107.61        1.21        124.87
Panel 3: No Increase in Sales & VMT criterion
Case 7: No rebound effect                        954.67        9.26           2.71       279.19        3.14        323.97
Case 8: Rebound elasticity = 0.1                 942.77        9.14           2.74       282.72        3.18        328.05
Case 9: Rebound elasticity = 0.2                 892.98        8.66           2.90       298.48        3.36        346.34
Panel 4: Increase in Sales & VMT Criterion
Case 10: No rebound effect                       949.55        9.21           2.72       280.70        3.16        325.71
Case 11: Rebound elasticity = 0.1                936.90        9.09           2.76       284.49        3.20        330.11
Case 12: Rebound elasticity = 0.5                884.06        8.58           2.92       301.49        3.39        349.84
Note: Total gasoline consumption reduction in cases 1-6 is given by the difference between equations (7) and (8) while that
in cases 7-8 uses the total VMT by new vehicles sold June-December of 2009 as the basis for comparison and adjusts the
VMT of new vehicles under the counterfactual scenario so that the total VMT under the two scenarios are the same.
Cases 1-3 and 7-9 assume that there is no net increase in new vehicle sales due to the program in the long run while cases
4-6 and 10-12 assume that the net increase is 30,579 units.




                                                            51
            Table 11: Estimated Effect of Cash for Clunkers on Vehicle Assembly and Parts Employment


                                 Geometric Function                         Logistic Function


                      Assembly           Parts        Total      Assembly         Parts         Total

                         (1)              (2)          (3)          (1)             (2)          (3)


Effects During June
                       1,732             1,944        3,676       1,690           1,897         3,587
 – December 2009


Effects During June     966              1,084        2,050       1,310           1,471         2,781
 2009 – May 2010

Effects During June
                        273               306         578          891            1,000         1,892
 2009 – May 2012




                                                       52

				
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